Tensorial is a general purpose tensor calculus package for Mathematica 5.0 or later. Easy to learn and convenient for students and researchers. The authors are Renan Cabrera, University of Windsor, Canada, David Park, and Jean-Fran├žois Gouyet, Ecole Polytechnique, Palaiseau France. Some of the features of Tensorial 4.0 are: Complete freedom in choosing tensor labels, indices and base indices. Flavored (colored or annotated) indices for various coordinate systems. Differently flavor indices may have different dimensions and base index sets. Minimum keystroke tensor input and formatted output that can be copied and pasted. Detailed set of index manipulation routines. Easy routines for setting tensor values or rules and expanding tensor sums and arrays. Zero tensors balance free indices, behave like zero and expand to zero arrays. CircleTimes and dot product routines. Routines to declare and apply tensor and tensor expression symmetries. Kronecker, generalized Kronecker and Levi-Civita routines. Partial, covariant, total, absolute and Lie derivative routines. Christoffel, Riemann, Ricci, Einstein, Weyl and scalar curvature routines. Conversions from coordinate basis to orthonormal basis. Dot mode routines to convert from index notation to Mathematica array form calculations. Blends naturally with the normal Mathematica notebook interface and kernel routines. Customizable. Complete documented Help with individual pages and examples for each command. Additional tutorial notebooks.